### Abstract

Let A be a superalgebra with graded involution or superinvolution ∗ and let cn∗(A), n = 1,2,…, be its sequence of ∗-codimensions. In case A is finite dimensional, in Giambruno et al. (Algebr. Represent. Theory 19(3), 599–611 2016, Linear Multilinear Algebra 64(3), 484–501 2016) it was proved that such a sequence is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ℤ2 and a 4-dimensional subalgebra of the 4 × 4 upper-triangular matrices with suitable graded involutions or superinvolutions. In this paper we study the general case of ∗-superalgebras satisfying a polynomial identity. As a consequence we classify the varieties of ∗-superalgebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth, and we give a full classification of their subvarieties which was started in Ioppolo and La Mattina (J. Algebra 472, 519–545 2017)

Original language | English |
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Pages (from-to) | 961-976 |

Number of pages | 16 |

Journal | Algebras and Representation Theory |

Volume | 22 |

Publication status | Published - 2019 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

La Mattina, D., Giambruno, A., & Ioppolo, A. (2019). Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions.

*Algebras and Representation Theory*,*22*, 961-976.